Lucasian Chair.org

• 17th Century
• 18th Century
• 19th Century
• 20th Century

• Isaac Barrow
• Sir Isaac Newton
• William Whiston
• Nicolas Saunderson
• John Colson
• Edward Waring
• Isaac Milner
• Robert Woodhouse
• Thomas Turton
• Sir George Biddle Airy
• Charles Babbage
• Joshua King
• Sir George Gabriel Stokes
• Sir Joseph Larmor
• P. A. M. Dirac
• Sir M. James Lighthill
• Stephen Hawking

"Everything that is really great and inspiring is created by the individual who can labour in freedom." Albert Einstein

An important professorship of mathematick was deeded in December 1663 at Cambridge University, England. A Member of Parliament for the university from 1639-1640, Mr. Henry Lucas, left instructions in his will for the purchase of land with a value that would provide an annual income of 100 pounds to support this professorship.

When the Chair was founded, people had only just begun to understand what the world was made of. Chemical elements were not yet discovered. Mathematics had yet to have calculus as a true tool. There were no thoughts of atom smashing and quarks or of relativity and anti-matter. A computer was a person who made calculations by hand. God was a certainty; the only question was which church did you belong to. Governments still had kings and queens. There were no superpowers with weapons of mass destruction. There were no airplanes and no space shuttle.

The three hundred and thirty years which have passed have witnessed changes in mathematics, science, technology, philosophy, religion and government. It is notable that the universities have not changed quite so much. One can still go to Cambridge to see where Newton spent his time. One can even see his original works in the library and at the Royal Society. The lineage of the professors who held the Lucasian Chair is unbroken from a time before the United States was a sovereign nation.

This has been a story of the unrelenting quest for knowledge and understanding through difficult times, yet with resounding success. It has demonstrated why universities have existed and must continue to exist. As Einstein has said, freedom is required for greatness to be achieved. Academic freedom is as important as any other freedom. The results of the freedom in a chair by its holder to create has been clearly demonstrated by the Lucasian Professorship.

The Lucasian Chair is only one chair, in one university, in mainly one discipline: mathematics, but it has influenced many other disciplines because mathematics is a fundamental discipline. There are many other chairs in many other universities for many other disciplines. This particular history has had more influence than most, but they all have a history that has had some influence on our world. Universities have been contributing to our world since the late twelfth century and hopefully will continue for many centuries more. The question still needs to be asked: what contribution?

The contributions of this Chair can be seen in several ways. Naturally the first is the contributions of each of the Chair's individual professors. Secondly, the tradition of the Chair itself is a contribution. People need a place to work, a focal point of some kind. The university environment has historically been a place, not just for learning (a student's perspective), but also a place for "professing" (a professor's perspective). There is an expectation that both are completely compatible. With people knowing, learning and teaching, this place acquires a third role, that of the keeper of knowledge over the centuries, so that new knowledge will come to this place to be shared with those who wish to learn. The new knowledge can be created at the university through research, but it can be just as easily created elsewhere. The university does not have a monopoly.

The traditions of knowledge are important for their own sake, not just for immediate application. History has shown that university-educated people can contribute after they leave the university in many ways soon after leaving. The real value, however, is over long periods of time. This is important for many reasons, but paramount is the amount of time it takes to create new knowledge, incorporate it and disseminate it. If we take the example of gravity, which Sir Isaac Newton first explained in his Principia, published in 1687, we find that the deep level understanding of it is still a problem. However, the knowledge and understanding produced by Newton most certainly has been used and developed to marvelous ends. The space program with its exciting successes of the moon landings, planetary exploration, the Space Shuttle and any future endeavors all depend on an understanding of how gravity works. Newton's work is used every day for many different reasons.

On the development side, the limits of Newton's explanation of gravity were reached at the beginning of the twentieth century because other people continued to work on the knowledge base. There are few large scale problems that are solved once and for all; continued extension is necessary for true understanding. This is the role that the tradition of the university as keeper of the knowledge is so important. The knowledge created by Newton, and gathered by Cambridge, was developed by people across the world for centuries. The continued creation and development has resulted in Einstein's Theory of Relativity with its tremendous impact on the overall understanding of how matter and energy make up the universe. Hawking is still working on gravity, along with many others, with the expectation that knowledge will be created, to be collected at the university and be disseminated to the next set of learners in the continuing quest for understanding.

This continuing quest has been in operation since the known beginnings of civilization. Some of the knowledge has been carved in stone or written on papyrus, but always the quest has been relentless. The gathering has examples in the distant past at places such the great library of Alexandria. Just as the forces that worked to stop the quest destroyed the library, they continue today to try to impede the knowledge industry. Fortunately people have an infinite thirst for understanding, not just in the sciences but in all human thought. One of the ways to impede the process today is through the withholding of money from those who would keep knowledge alive. One of the tools to fight this is through the endowed chair, such as the Lucasian Chair.

The Chair has produced some specific ideas and tools that have resulted in technology useful in our lives, but one of the major contributions has been the three hundred plus years of a place for top mathematicians to be. It has withstood the greats and not so greats. After Newton, Britain experienced a long period of about one hundred fifty years where no groundbreaking mathematician was produced. Europe, on the other hand, produced a number of tremendously talented mathematicians, many of whom worked on problems identified by Newton. The general system of universities continued, even though in this one place, progress was slowed down. It should be pointed out that although progress was slowed in Britain, it was not stopped. Eventually Britain recovered and began to contribute again, with the Lucasian Chair producing its share of the knowledge.

During this drought in Britain, the tradition continued to live. The students were taught and went out into the world until the recovery took place. Cambridge and England have done well ever since. This part of the Chair's history demonstrates further how important it is to keep the endowed chair alive, even when the short-term assessment of the situation is not a good one. The strength of a chair is seen in both its productivity and its longevity. Even during the drought, the Lucasian Chair had bright spots and points that were trying to overcome the difficulties. The eighteenth century was the most troublesome, following directly after Newton. The Chair did show its helping hand when John Colson produced translations from several languages to spread the knowledge. At the end of the century, Edward Waring tried to help develop algebra, but he was struggling against overwhelming odds. He was unable to move Britain's mathematics forward, but his legacy is present in his works. He presented problems that were not mathematically proven for almost two centuries. He was a first-class mathematician who used both forms of the notation for calculus, unlike the majority who used only Newton's notation.

In the beginning of the nineteenth century Robert Woodhouse published his mathematics with explanations of why Britain had made the wrong choice in the style of notation used for calculus. Although he was unable to move Britain in general, his students eventually did just that. Charles Babbage and others moved Cambridge to the proper notation. This in turn set the direction for new Cambridge students. The lock by the forces holding back British mathematics was broken in the middle of the century. The last occasion of the struggle was the professor who followed Babbage in the Chair, Joshua King. King did not produce any work, generally using the Chair as a sinecure. Fortunately, after King came Sir George Stokes, a brilliant, responsible and capable man. The tide was turned forever. The Chair had been raised to its proper level.

The problem of calculus notation is a good example of how a feeling of a problem being solved once and for all is a danger. The tradition is one where new knowledge refines and extends old knowledge. The value of old knowledge is not diminished by new knowledge, unless the old was simply wrong. Even then, there is value to its preservation for the historical perspective. But it cannot be assumed that once a fundamental problem is solved, that the process comes to an end. In fact, it is the opposite; it is a door opened up to more knowledge. Perhaps when we know everything there is to be known, we will know what to do at the end of the process. Until then there is a role for chairs and institutions of higher education.

The role of these institutions is as a participant in the ongoing process, but there are meta-roles as well. During the Dark Ages the early versions of higher education nursed and protected the process to keep knowledge alive. Since Newton, newer versions have nurtured the process for growth, as a participant in the Scientific Revolution. The current versions are faced with new challenges. The societal pressures, caused in part by the process itself, are powerful and threatening. Universities are playing an increasing role in the production of useful knowledge, not just knowledge for its own sake. When Newton understood gravity, it was not because he envisioned trips to Mars, but it was because understanding was what he did for a living. It was only later that others used his understanding for practical purposes. Today we have much understanding that has been turned into practical uses, not all of which are good. The Scientific Revolution is not slowing down, but it is reaching a point where it is difficult for the average person to cope with it. The problem comes in two parts, one is that the average person simply does not have the background to understand and appreciate the existing knowledge. The second part is the threat posed by the knowledge taking on a life of its own and moving forward with no regard for those who are in the way.

Just as during the Industrial Revolution the average person suffered job loss and poverty as technology moved forward, the twenty-first century will do the same. The problems have, in fact, already begun. The difficulties caused by economic problems, whose source is in the shift of the capability and use of current technology, affect the universities. The financial pressures have only grown during this century and do not show any signs of abating. The possibility of a new Dark Ages is quite real. Universities need more than ever to protect their roles in the face of these pressures. The endowed chairs will be able to survive, as long as the place they operate from survives. Without these chairs it will be difficult for universities to resist the temptation to offer programs without content to simply keep the cash flow positive.

Stephen Hawking has been able to bring science to the public to help with the first problem, understanding by the average person. He has been involved with popular books, popular television, film and public appearances, different from the reclusive Sir Isaac Newton. It is not an easy task for a professor to stem the tide of technological progress, however. Cambridge and the Lucasian Chair will face a great challenge when Hawking one day relinquishes the Chair. It will be an important event in the Chair's history, perhaps even a major turning point.

Mathematics has developed considerably since Newton and Barrow held the Chair. It is really a tool to be used by other disciplines. Its development in the history of the Lucasian Chair is quite evident, with the early professors working on geometry and algebra and Newton bringing together the rules so that calculus became useable. Since that time the strict adherence to mathematics for itself has given way to mathematics applied to other pursuits. Beginning with Sir George Airy, application has been foremost in the professor's activities. He was an astronomer and was followed by Babbage whose application of mathematics extended to insurance, railroads, and computing. This change in direction was of importance for the Chair. The change was interrupted by King's tenure, but reverted back with Stokes. He used mathematics for the understanding and explanation of fluids. Fluid mechanics was still considered physics at the time.

Physics and fluid mechanics are two disciplines that depend highly on mathematics. It is virtually impossible to understand either fully without an equivalent understanding of mathematics. The Chair is well served by the occupancy of physicists and fluid mechanists, at least for the past one hundred and fifty years. Will it continue to be as well served by following in the same tradition in the future? The question arises because the need for mathematics to develop for deeper understanding is not there at the moment. There is enough to work with now. This may not be true for very long, but no one is complaining because the mathematical tools are holding them back. The main problem seems to be in the technology that allows the math to be fully utilized: computers. Computers are certainly quite good today, and far superior to even a few years ago, but to make serious progress in the calculations used for understanding matter and energy, much more powerful machines are necessary. The time is coming when the hardware that provides the base for computing will reach its limits. Smarter use of the hardware is required, but even more than that is the need for smarter software. Once everyone has the fastest possible automobile, for example, it is the driver that makes the difference in a race. Once one has the fastest computer hardware, the intelligence that makes it work better will be found in the software, the instructions that tell the hardware and other software what to do. One of the best use of mathematics is for just this purpose.

Physics has had its best days in terms of support by taxpayers in the USA. There was almost a no-questions-asked policy for the years following the development of the atomic bomb in World War II. Physics had created a tremendous weapon that ensured military support for many years. These years seem to be coming to a close. Basic research is still supported, but not at the equivalent levels and not without difficulty. In fact, the termination of the Super Collider program is a clear signal that this is true. Even physics must justify itself from the same vantage point as other sciences. Two areas are still growing, however, biology and technology. Biology does not make use of mathematics to a large extent, but technology does, especially computers. It would seem to be in step with history if the next Lucasian professor were a mathematician whose speciality was related to computation.

Britain has shown a kind of stubbornness to cling to its past, even in the face of obvious need to move forward, but it has always moved eventually. When it has moved, it has moved well. Just as Newton was the shining example of the genius of his times, perhaps Cambridge can find someone to fill his shoes in the tradition, not of the discipline, but in the tradition of a university as the focus of knowledge development. Mathematics has both a theoretical side and a practical side. Often it takes many years before an idea finds practical application, if ever. These ideas that are developed to help understand a particular problem are still important. Calculus was a practical use of mathematics, in Newton's time as well as our own. Some of Waring's problems dealing with prime numbers were not so easily applied. It took a century and a half to even understand what he had said and to write the proof. It is today that this work is finding a use. The use is in computing application.

The work of some of the Lucasian professors has been immediately practical, such as Lighthill's work in aviation, but some has not been so, such as that of Waring and Hawking. It is an interesting balance to maintain between the applied and the theoretical, but I believe the time is for leadership in pushing the boundaries further in the applied arena, especially in computation, for computation has more promise for humanity than physics. The great theories of the future will require tools, just as the great theories of the past have required tools. The difference is the availability of the tools. These tools can be limited by how much we know or how much we can produce. We know quite a lot and we can produce quite a lot. I believe it is time to do this. A university chair is a good place to start.